Analysis of PIV measurements using modal decomposition techniques, POD and DMD, to study flow structures and their dynamics within a stirred-tank reactor

Abstract

The present work is a comparative analysis of Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) computed on experimental turbulent velocity fields measured in a 20L-tank stirred by two Rushton impellers at two rotating speeds, N = 150 and 300 rpm. POD identifies flow structures that optimally capture the total kinetic energy of the flow, while DMD identifies structures that significantly contribute to the dynamics of the flow. The experimental data, i.e. the instantaneous velocity fields Ur(r,z,t) and Uz(r,z,t), come from 2-D Particle Image Velocimetry (PIV). The flow motion is turbulent, and it occurs over a wide range of length and time scales, from equipment-dependent large-scale coherent structures to the smallest-scale eddies where energy dissipation takes place. It thus provides an interesting benchmark case for the comparison between POD and DMD, which are based on energy and dynamic analysis, respectively. POD analysis reveals that the most energetic structures are related to the inherent periodic unsteadiness due to the relative motion between the rotating impeller blades and the non-moving baffles. Apart from the mean field, the first most energetic group of modes is related to trailing vortices induced by the Rushton turbines and is associated to a frequency equivalent to the blade passage frequency and its overtones. The second most energetic group of modes is related to vortical structures in the impeller stream and is associated to a frequency equivalent to the rotating speed. DMD analysis identifies flow structures that are found similar to these most energetic modes, although differences appear due to the fact that DMD isolates structures associated to a single frequency and their corresponding growth/decay rate. As in POD, the relative importance of each DMD mode can be estimated using an appropriately defined energy criterion. Comparison of the results from both modal decomposition methods points out their complementarity and their potential for describing the spatial and time characteristics of the flow within a stirred tank.